Find the surface area or volume.
-Use an integral table and a calculator to find to two decimal places the area of the surface generated by revolving the curve $y = x ^ { 2 } / 2 , - 3 \leq x \leq 3$, about the $x$-axis.
A) 114.20
B) 196.27
C) 140.14
D) 160.59

Question

Quizplus · Accepted Answer

The surface area $S$ generated by revolving a curve $y = f(x)$ about the x-axis from $x = a$ to $x = b$ is given by the formula $S = 2\pi \int_{a}^{b} y \sqrt{1 + (dy/dx)^2} dx$. For $y = x^2/2$, $dy/dx = x$, so the formula becomes $S = 2\pi \int_{-3}^{3} (x^2/2) \sqrt{1 + x^2} dx$. Solving this integral gives the surface area as approximately 140.14 square units.

Find the Surface Area or Volume y=x2/2,−3≤x≤3y = x ^ { 2 } / 2 , - 3 \leq x \leq 3y=x2/2,−3≤x≤3

Find the Surface Area or Volume $y = x ^ { 2 } / 2 , - 3 \leq x \leq 3$